http://www.employees.org/~calridng/allsites.html is alink with many of California's riding areas.
I moved here about 4 yeas ago but with two young kids, have not been riding much. I am from Northern Cal and prefer the woods. Most people around here go over to the desert.
Until recently, the open land on the northeast of town was a popular spot to go ride, but it is now being developed and posted no trespassing. Some people drive out to Taft and ride in the oil fields there, about 1/2 hour SW of town. If you are used to great single track, it's hard to get excited about riding there.
Hungry Valley State Vehicle Recreation Area (Gorman) is about 45 - 60 minutes south. Most of the park is quad trails, but there are some good single track in the mountains.
Ballinger Canyon has about 70 miles of trails and 1/3 of that is single track. It is about 60 - 75 minutes drive, SW of town.
I have not been to Jawbone Canyon, but it is about 1.25 - 1.5 hours east of town and is reported to have lots of good riding.
There is abundant riding in the desert within 1.5 - 2 hours drive east.
Clear Creek (the site of the Quicksilver National enduro) is about 2.5 hours northwest. It is an awesome place to ride if you go with someone who knows the area.
Kennedy Meadows (the Kern Plateau) is at the headwaters of the Kern River, which runs through Bakersfield. It is about 2.5 hours or more drive. I have not been there in many years, but it is awesome forest riding. It's about 9,000 feet elevation and you can usually only ride there from June to September.